Answer:
Part A) The length of a straight line between the school and the Fire Station is [tex]4.6\ miles[/tex]
Part B) The length of a straight line between the school and the hospital is [tex]2.1\ miles[/tex]
Step-by-step explanation:
The complete question in the attached figure
Let
The positive x-coordinates ----> East
The positive y-coordinates ----> North
The negative x-coordinates ----> West
The negative y-coordinates ----> South
take the point A (0,0) as the Middle School (reference point)
Part A) we have
Town Hall is located 4.3 miles directly east of the Middle School
so
The coordinates of Town Hall are B(4.3,0)
The Fire Station is located 1.7 miles directly North of Town Hall
so
The coordinates of Fire Station are C(4.3,1.7)
What is the length of a straight line between the school and the Fire Station?
Remember that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
A(0,0) and C(4.3,1.7)
substitute
[tex]d=\sqrt{(1.7-0)^{2}+(4.3-0)^{2}}[/tex]
[tex]d=\sqrt{(1.7)^{2}+(4.3)^{2}}[/tex]
[tex]d=4.6\ miles[/tex]
Part B) we have that
The hospital is 3.1 miles west of the fire station
so
The coordinates of the hospital are D(4.3-3.1,1.7)
D(1.2,1.7)
What is the length of a straight line between the school and the hospital?
Remember that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
A(0,0) and D(1.2,1.7)
substitute
[tex]d=\sqrt{(1.7-0)^{2}+(1.2-0)^{2}}[/tex]
[tex]d=\sqrt{(1.7)^{2}+(1.2)^{2}}[/tex]
[tex]d=2.1\ miles[/tex]
